Learning GoalsAfter completing this lesson, you should be able to answer the following questions:

• What types of objects make up our Solar System?• How were the sizes of the Earth and Moon first determined?• How do the sizes of the other planets compare to Earth?• How does the size of the Sun compare to the sizes of the planets? to Earth?• How can we determine the distance to the Moon? to the Sun?• How do the distances to the Moon and Sun compare to the size of the Earth, or

other celestial objects?• How does the spacing of the planets change with distance from the Sun?• How do the orbits of the planets compare in terms of eccentricity and inclination?

There’s No Place Like Home

As we begin the course, the best place to start is right here at home, our planet Earth. You may have learned that the general public believed that we lived on a flat Earth until Christopher Columbus proved otherwise, but this is not true. We have known that the Earth is round for thousands of years. How did we determine this?

When we look up into the heavens, probably the two most obvious observations are those of the Sun and the Moon. You may notice that they both appear to be roughly the same size in the sky, but as we’ll quickly find out, they are not actually the same diameter. How can we determine their sizes, and how far away they are from us?

Finally, we’ll also look at the other planets in our solar system, see how they compare to ours in size, and find out where they are located and how they move around the Sun. By the end of this lesson, you should have a good feel for the size and scale of our solar system, the place we call home.

Basic Facts

The Solar System is composed of:• 1 Star – the Sun• 9 Major Planets – Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune & Pluto• Dwarf Planets – 5 officially classified so far (Ceres, Pluto, Haumea, Makemake & Eris)• Over 100 Moons (and counting)• Asteroids, Comets, Meteoroids, and other objects!

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Diameter of the Earth

Eratosthenes was able to determine that the Earth was round and measure the size of the Earth with a few simple measurements and geometric calculations.

Eratosthenes discovered that at noon on the summer solstice, a vertical stick in the city of Syene cast no shadow, while at the same time, a shadow was cast in the more northern town of Alexandria.

While most people believe that it was Christopher Columbus who determined that the Earth was round, knowledge that the Earth was round was known by some for over a 1000 years beforehand!

Diameter of the Earth

Eratosthenes was able to determine that the Earth was round and measure the size of the Earth with a few simple measurements and geometric calculations.

Eratosthenes discovered that at noon on the summer solstice, a vertical stick in the city of Syene cast no shadow, while at the same time, a shadow was cast in the more northern town of Alexandria.

If the Earth were flat, then the shadow cast by a vertical stick would be the same everywhere. The fact that the shadow differed between cities suggested that the Earth was round.

Using basic geometry, Eratosthenes was able to calculate the circumference, and from that the radius, of the Earth. The distance between Syene and Alexandria is a fraction of the total circumference of the Earth. The angular difference between the shadows equals the difference in latitudes of the two cities,

which is a fraction of a complete 360o circle.

C = 250,000 stadia = 46,000 km (Actual circumference: 40,007.86 km; radius = 6378.1 km)

While most people believe that it was Christopher Columbus who determined that the Earth was round, knowledge that the Earth was round was known by some for over a 1000 years beforehand!

360

2.75000

C

stadia

Moon’s orbit

Diameter of the MoonWe can use basic geometry to determine the sizes of and distances to other celestial objects as well.As we’ll find out in a later lesson, every once in a while the Moon passes directly between the Earth and Sun, casting a shadow upon the Earth, which has a diameter of around 100 km (practically zero, compared to the size of the Moon).Sometimes, when the Moon is on the other side of the Earth from the Sun, it passes through the Earth’s shadow. When it does, we can observe that the Earth’s shadow is roughly 2.5 times wider than the Moon.

Light rays from lower edge of sun

Light rays from upper edge of sun

Earth’s shadow is 2.5 times wider than Moon

Moon during lunar eclipse

Earth

Moon during solar eclipse

Moon’s shadow tapers 1 moon diameter

Earth

2.5 Moon Diameters 2.5 Moon

Diameters

If the shadow of the Moon tapers from one moon-diameter to essentially zero over the same distance that the Earth’s shadow tapers to 2.5 moon-diameters, that suggests that the Earth is roughly 3.5 moon-diameters big, or 3.5 times bigger than the Moon.

In actuality, the Earth is 3.67 times bigger than the Moon.(radius of the Moon = 1737.4 km)

Moon

3.5 Moon Diameters

Radius of Moon’s Orbit

Diameter of the Moon

Astronomers have also determined the sizes of the planets. Below are the terrestrial planets (plus the Moon), shown to scale. Out of all of the terrestrial planets, Earth is the largest.

As you can see, Venus is only slightly smaller than Earth.Mars is roughly half the size of Earth.Mercury is about 40% the size of Earth.The Moon is a little more than a quarter the size of Earth.

Planetary Sizes

Planetary SizesBelow are the Jovian planets (plus Earth), shown to scale. The Jovian planets are all much larger than Earth (the largest terrestrial planet).

Uranus and Neptune are roughly 4 times bigger than Earth.

Saturn is 9.5 times bigger than Earth.

Jupiter is over 11 times bigger than Earth!

Earth

The sizes of all of the planets are negligible compared to the Sun. The Sun has a diameter of around 1.4 million km. This means that you could fit 109 Earth’s end-to-end across the diameter of the Sun. How many Jupiters would it take to span the diameter of the Sun?

In terms of volume, you could fit over one million Earth’s inside of the Sun.

Diameter of the Sun

Distance to the Moon

To determine the distance to the Moon, we can use similar triangles.

If you’ve ever looked at the Moon when its high in the sky, you may have noticed that it appears to be about the size of a quarter held at arms length (try it some time – hold up a quarter next to the Moon and compare).We can see in the figure below that there are two triangles: in each one, the long sides represent the distance to the object (coin or Moon) and the short side represents the diameter of the object.Using similar triangles, the ratio of the diameters is equal to the ratio of the distances. Using this method, we can determine the distance to the Moon.

Distance to MoonDistance to coin

Diameter of coin

Diameter of Moon

Coin diameter Moon diameterCoin distance Moon distance

The Earth-Moon System

So how far away is the Moon from the Earth?

It would take around 30 Earths, lined up side-by-side, in order to reach the orbit of the Moon. In other words, the diameter of the Moon’s orbit (from one side to the other) is equal to 60 Earth diameters.

Based on this, which is bigger, the Moon’s orbit, or the diameter of the Sun?

Earth

Moon

To Scale

Distance to the Sun

Now that we know the distance to the Moon, we can determine the distance to the Sun.

At certain times, the Moon (as viewed from Earth) will appear to be half-illuminated. We call this a Quarter Moon (we’ll discuss this more in a later lesson). The Moon will appear in this phase when the angle between the Earth & Sun is exactly 90o.

If we measure the angle between the Moon and Sun at this time, we can use basic trigonometry to determine the distance to the Sun.

Sun

Quarter Moon

Earth

90°

XD

€

cosθ =D

X

X =D

cosθ

NOT TO SCALE

The Sun-Earth SystemSo how far away is the Earth from the Sun?

It would take almost 108 Suns, lined up side-by-side, in order to reach the orbit of the Earth. (Sorry, I’m not drawing that one to scale).How many Earths would it take, lined up side-by-side, to span this distance?

We define the average distance between the Earth and the Sun as one astronomical unit (AU). 1 AU roughly equals 1.5 x 108 km, or 150 million kilometers.

Earth

Not To ScaleSun

1 AU

Spacing of the Planets

The planets are not evenly distributed through space. The spacing increases as you move farther out in the solar system.Below is a scale model of the spacing of the planets in our solar system, compared to a football field. (The scale is 100 in = 1 AU)

NOTE: Only the spacing is to scale; the sizes of the planets and the Sun are not to scale.

102030 40 50 40 302010

20 3040504030 20 1010

Mer

cury

Ven

usE

arth

Mar

s

Jupi

ter

Sat

urn

Ura

nus

Nep

tune

Ast

eroi

d B

elt

Kui

per

Bel

t

Orbital Properties

Not all of the planets orbit in exactly the same plane as the Earth (what we call the ecliptic plane), but relative to the ecliptic plane, most other planets orbit close to the same plane. The most inclined is Mercury at 7º.

Based on our understanding of how the solar system formed, this is to be expected. All of the planets formed out of the material which formed around the Sun, which, as we’ll find out later, collapsed down into the shape of a disk.

Orbital Properties

The planets all orbit around the Sun in the same direction; counterclockwise when viewed from above Earth’s north pole (and most moons orbit around their planet the same way).

Most planets have near circular orbits. The most eccentric is Mercury with an eccentricity of e = 0.21.